Such a method and the corresponding apparatus having a measuring probe containing the projector and the camera are known from U.S. Pat. No. 4,952,149 and are described there with the aid of an exemplary embodiment on the basis of the projection of the pattern by means of parallel light beams (telecentric projection). Mentioned briefly, moreover, as an alternative, is the projection with the aid of diverging light beams (central projection).
Both the telecentric and the central projection are represented here in FIGS. 1 and 2.
As FIG. 1 shows, in the case of this known method a stripe pattern M.sub.P located in the plane of projection PE of the projector and with sinusoidal brightness distribution transverse to the stripe direction is projected by means of the parallel light beams L at the angle of incidence .alpha. onto the object to be measured, represented by the object plane OE, and also onto a reference plane RE and the respective images M.sub.OE and M.sub.RE are taken up by the camera, that is, imaged on the sensor surface SF thereof. The difference between the phase positions determined from the two takes for each camera-side image point BP.sub.K or the path difference .DELTA.x between the sinusoidal waves of the two patterns M.sub.OE and M.sub.RE is, in accordance with the equation tg.alpha.=.DELTA.x/.DELTA.z, a direct measure of the distance .DELTA.z between the reference plane RE and the object-side image point BP.sub.O imaged on the object or on the corresponding object surface point. Since the angle of incidence .alpha. is the same for all projected light beams, the range of validity of this equation extends to all object surface points encountered by the projected light bees.
In view of the telecentric projection, the projector used requires an optical system, the diameter of which is at least equal to the diagonals of the surface on the object to be illuminated. The result of this, for the measurement of teeth in the patient's mouth, is undesirably large dimensions and, consequently, insufficient ease of handling of the measuring probe.
In contrast therewith, the measuring probe or the projector with the optical system formed for the central projection is of considerably smaller dimensions and is thus better suited for the measurement of teeth in the patient's mouth. The diverging beam course of this optical system is disadvantageous though in so far as it excludes the use of the above-mentioned relationship between phase difference and the distance .DELTA.z. The stripe pattern M.sub.RE or M.sub.OE respectively projected onto the reference plane RE or the object plane OE is namely distorted, as shown in FIG. 2, in comparison with the stripe pattern M.sub.PE located in the plane of projection PE in accordance with the different angles of incidence .alpha.,.beta. of the individual light beams L. In other words, the camera no longer observes a displacement of the reference plane by .DELTA.z, as in the case of telecentric projection, as the sole displacement of the phase position of the stripe pattern, but as a mixture of phase displacement and different change of the wavelength. Thus the distance values .DELTA.z determined, in the same way as the contour image of the object derived from them, contain different error contents corresponding to the different distortions of the wavelength.